My question is about astrological compatibility in concern as to choosing one’s life partner. Should one consider astrological compatibility to have importance in the aspect of advancement in grhasta asrama?

First, there are too many divorced astrologers. Also, probably most divorced devotees went to an astrologer before marriage. Good marriages are based on mutual understanding, mutual respect, and mutual dedication. Compatibility is important, and astrology may help, but we are servants of Krishna, not astrology.